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lfunc_lfunctions • Show schema
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{'Lhash': '3297879173153212415846779213635', 'a10': [5.7270223163051455, -15.734864494761094], 'a2': [-0.6916028120303691, -1.9001631092847586], 'a3': [1.7057370639048863, 0.3007674663608706], 'a4': [-0.0681276198024956, 0.05716586064926002], 'a5': [6.343458332889615, 5.322793547516119], 'a6': [-0.6081853059290739, -3.4491902684741915], 'a7': [-5.237898938651108, -9.072307086654817], 'a8': [-6.849057463183484, -3.9543051700642], 'a9': [2.8190778623577253, 1.0260604299770062], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5531375068536926, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.7057370639048863, -0.3007674663608706]]], [19, [[1.0, 0], [17.676982969332506, -6.9659366277571415]]]], 'bad_primes': [3, 19], 'central_character': '57.52', 'coefficient_field': 'CDF', 'conductor': 57, 'conductor_radical': 57, 'conjugate': '2632170628618620011512733194416', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'sign_arg': {'__RealLiteral__': 0, 'data': '0.17109268169', 'prec': 44}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.60156794984316508011045666982', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.59949311099713699911390287109', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.27027308879680087606627968060', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5531375068536926, 'bad_primes': [3, 19], 'central_character': '19.14', 'conductor': 57, 'conductor_radical': 57, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/57/3/k/b/52/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-57-19.14-c2-0-3', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-57-19.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.246249375868928, 'root_angle': 0.17109268168976025, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.60156794984316508011045666982', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3297879173153212415846779213635', 'Lhash_array': ['3297879173153212415846779213635'], 'label': '2-57-19.14-c2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/57/3/k/b/52/2'}